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Curt Jaimungal

06/06/25

@ Curt Jaimungal

Defining energy in general relativity is complex; pseudotensors can provide conservation but break covariance, while covariant definitions work under symmetry but fail in general spacetimes, hinting at a deeper structure yet to be universally interpreted.

Video

What is “Energy,” Actually?

@ Curt Jaimungal

What is “Energy,” Actually?

06/06/25

Related Takeaways

Curt Jaimungal

06/06/25

@ Curt Jaimungal

Einstein introduced the pseudotensor to represent the energy of the gravitational field, but it depends on chosen coordinates, which contradicts the principle of general covariance.

Curt Jaimungal

06/06/25

@ Curt Jaimungal

In flat spacetime, energy-momentum conservation is straightforward, but in General Relativity, it becomes complex due to the need for a covariant derivative and additional machinery.

Curt Jaimungal

06/06/25

@ Curt Jaimungal

If spacetime has symmetries, such as a timelike Killing field, it allows for the definition of genuinely conserved, coordinate-independent energy.

Curt Jaimungal

06/06/25

@ Curt Jaimungal

Most realistic cosmological spacetimes lack exact Killing vectors, limiting the applicability of the clean definition of energy in General Relativity.

Curt Jaimungal

06/06/25

@ Curt Jaimungal

The relationship between matter and curvature in Einstein's equations suggests that only matter energy is well-defined, leaving the nature of energy in general relativity still unresolved after over a century of inquiry.

Curt Jaimungal

06/06/25

@ Curt Jaimungal

Definitions of energy, such as mass in motion or the capacity to change, don't hold up in dynamically curved spacetime.

Curt Jaimungal

06/06/25

@ Curt Jaimungal

The energy associated with gravity is coordinate-dependent, raising questions about whether this is a valid justification for using the pseudotensor.

Curt Jaimungal

06/06/25

@ Curt Jaimungal

In the context of the expanding universe, the standard energy is not conserved as energy gets diluted, but a vector field can be found that satisfies conservation conditions, leading to a conserved quantity related to entropy.

Curt Jaimungal

06/06/25

@ Curt Jaimungal

Gravitational waves, while detected by LIGO and predicted to carry energy, present a challenge in general relativity because covariant definitions based on stress energy yield zero energy for pure gravitational waves.